We have developed methods for performing qudit quantum computation in the Jaynes-Cummings model with the qudits residing in a finite subspace of individual harmonic oscillator modes, resonantly coupled to a spin-1/2 system. The first method determines analytical control sequences for the one-and two-qudit gates necessary for universal quantum computation by breaking down the desired unitary transformations into a series of state preparations implemented with the Law-Eberly scheme [1]. The second method replaces some of the analytical pulse sequences with more rapid numerically optimized sequences. In our third approach, we directly optimize the evolution of the system, without making use of any analytic techniques. While limited to smaller dimensional qudits, the third approach finds pulse sequences which carry out the desired gates in a time which is much shorter than either of the other two approaches. * brianm@phys.au.dk 1 arXiv:1210.4488v1 [quant-ph]

We demonstrate accurate single-qubit control in an ensemble of atomic qubits trapped in an optical lattice. The qubits are driven with microwave radiation, and their dynamics tracked by optical probe polarimetry. Real-time diagnostics is crucial to minimize systematic errors and optimize the performance of single-qubit gates, leading to fidelities of 0.99 for single-qubit π rotations. We show that increased robustness to large, deliberately introduced errors can be achieved through the use of composite rotations. However, during normal operation the combination of very small intrinsic errors and additional decoherence during the longer pulse sequences precludes any significant performance gain in our current experiment.

We study the ability to control d-dimensional quantum systems (qudits) encoded in the hyperfine spin of alkali-metal atoms through the application of radio-and microwave-frequency magnetic fields in the presence of inhomogeneities in amplitude and detuning. Such a capability is essential to the design of robust pulses that mitigate the effects of experimental uncertainty and also for application to tomographic addressing of particular members of an extended ensemble. We study the problem of preparing an arbitrary state in the Hilbert space from an initial fiducial state. We prove that inhomogeneous control of qudit ensembles is possible based on a semi-analytic protocol that synthesizes the target through a sequence of alternating rf and microwave-driven SU (2) rotations in overlapping irreducible subspaces. Several examples of robust control are studied, and the semi-analytic protocol is compared to a brute force, full numerical search. For small inhomogeneities, < 1%, both approaches achieve average fidelities greater than 0.99, but the brute force approach performs superiorly, reaching high fidelities in shorter times and capable of handling inhomogeneities well beyond experimental uncertainty. The full numerical search is also applied to tomographic addressing whereby two different nonclassical states of the spin are produced in two halves of the ensemble. * bmischuck@gmail.com 2